Derivation of optical solitons and other solutions for nonlinear Schrödinger equation using modified extended direct algebraic method

Optical solitons is one of the fastest growing areas of research in the field of nonlinear fiber optics. In the current work, the modified extended direct algebraic method is implemented to obtain optical solitons for the nonlinear Schrödinger’s equation with group velocity dispersion and second order spatiotemporal dispersion that describe the propagation of optical solitons in nonlinear media. Bright soliton solutions, dark soliton solutions and singular soliton solutions are obtained. Also, periodic solutions, exponential solutions, Jacobi elliptic solutions and Weierstrass elliptic solutions are extracted. Under specific parameter values, 2D, 3D and contour graphs are introduced to visualize the model and demonstrate their accurate physical behaviors.